Finite Group Databasebeta

← #21447494

Subgroups — #21447494

Order 7808.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839736C212yesmaximal
2#16839557C214yesmaximal, complemented
3C61×#536C211yesmaximal, characteristic
4#14519736—22no—
5#14519692—22no—
6#14519692C2214yes—
7C2×#41×C61C2211yescharacteristic
8C22×Q8×C61C411yescharacteristic, complemented
9C4⋊Q8×C61C412yescomplemented
10#124×C61C2212yes—
11#123×C61—22no—
12C22⋊Q8×C61—22no—
13#117×C61C411yescharacteristic, complemented
14#41×C61—42no—
15C2×Q8×C61—21no—
16C2×Q8×C61—42no—
17C2×Q8×C61C2×C412yes—
18C2×Q8×C61C2×C411yescharacteristic
19C2×D4×C61D412yes—
20C2×D4×C61C2311yescharacteristic
21C22×C4×C61—21no—
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61D412yes—
24C4⋊C4×C61—21no—
25C4⋊C4×C61—24no—
26C22⋊C4×C61—21no—
27C22⋊C4×C61—24no—
28C42×C61C2×C412yes—
29C22⋊Dic61—24no—
30C4⋊Dic61—42no—
31C4×Dic61—42no—
32C23×C61C22⋊C411yescharacteristic
33C23×C61C2×D412yes—
34Q8×C61—41no—
35Q8×C61—42no—
36Q8×C61—42no—
37D4×C61—42no—
38D4×C61—41no—
39C2×C4×C61—22no—
40C2×C4×C61—22no—
41C2×C4×C61—22no—
42C2×C4×C61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—42no—
45C2×C4×C61C22⋊C412yes—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22×C411yescharacteristic
48C2×Dic61—44no—
49C22×C61—22no—
50C22×C61—21no—
51C22×C61—41no—
52C22×C61—42no—
53C22×C61C2×C22⋊C411yescharacteristic
54C4×C61—22no—
55C4×C61—21no—
56C4×C61—42no—
57C4×C61—42no—
58C4×C61#9912yes—
59Dic61—84no—
60#2129—611nomaximal, Sylow
61C2×C61—21no—
62C2×C61—42no—
63C2×C61—41no—
64C2×C61C2×#9911yescharacteristic
65#536D6111yescharacteristic
66#410—612no—
67#354—614no—
68C61#212911yescharacteristic, complemented, Sylow
69C2×#41C2×D6111yescharacteristic
70C22×Q8Dic6111yescharacteristic, complemented
71C4⋊Q8Dic6112yescomplemented
72#124C2×D6112yes—
73#123—22no—
74C22⋊Q8—22no—
75#117—1222no—
76#117Dic6111yescharacteristic, complemented
77#99—614no—
78#99—1222no—
79#41—42no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8C2×Dic6112yes—
83C2×Q8C2×Dic6111yescharacteristic
84C2×D4C22⋊D6112yes—
85C2×D4C22×D6111yescharacteristic
86C22×C4—21no—
87C22×C4C2×Dic6111yescharacteristic
88C22×C4C22⋊D6112yes—
89C4⋊C4—24no—
90C4⋊C4—21no—
91C4⋊C4—2442no—
92C22⋊C4—21no—
93C22⋊C4—24no—
94C22⋊C4—1224no—
95C42—2442no—
96C42C2×Dic6112yes—
97C23C22⋊Dic6111yescharacteristic
98C23C2×C22⋊D6112yes—
99Q8—41no—
100Q8—42no—
101Q8—42no—
102D4—42no—
103D4—41no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—2444no—
111C2×C4C22⋊Dic6112yes—
112C2×C4C22⋊Dic6111yescharacteristic
113C2×C4C22×Dic6111yescharacteristic
114C22—21no—
115C22—22no—
116C22—41no—
117C22—42no—
118C22C2×C22⋊Dic6111yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C4—4884no—
124C4#1451969212yes—
125C2—21no—
126C2—42no—
127C2—41no—
128C2C2×#1451969211yescharacteristic
subgroupG/H
centerC2C2×#14519692
commutatorC2×C4×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#536C2
socleC2×C61C2×#99
hypercenter#536D61
hypocenterC61#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #16839557C2semidirect
8. C22×Q8×C61C4semidirect
9. C4⋊Q8×C61C4semidirect
13. #117×C61C4semidirect
68. C61#2129semidirect
70. C22×Q8Dic61semidirect
71. C4⋊Q8Dic61semidirect
76. #117Dic61semidirect